Use the aggregate function SFTEST to perform the Shapiro-Francia test for the composite hypothesis of normality. The test statistic of the Shapiro-Francia test is simply the squared correlation between the ordered sample values and the (approximated) expected ordered quantiles from the standard normal distribution. The p-value is computed from the formula given by Royston (1993).

Syntax

Arguments

@x

the sample values. @x is an expression of type float or of a type that can be implicitly converted to float.

@statistic

identifies the return value as either the Shapiro-Francia statistic (w) or the p-value (p).

Return Types

float

Remarks

·If @x is null then @x is not included in the aggregate.

·@statistic must be invariant for the GROUP.

·SFTEST is an aggregate function and follows the same conventions as all other aggregate functions in SQL Server.

·@x must have at least 3 rows

Examples

In this example, we have two samples, which we have identified as sample 1 and sample 2 and we perform the Shapiro Francia test on both in a single SELECT, grouping the results by sample number.